كَمْ ضَرَبْتَ؟ — How many times did you strike?
Expanded meaning: «كَمْ ضَرْبَةً ضَرَبْتَ؟»
ضَرْبَةً: the understood tamyīz when made explicit; accusative.
Here kam counts the occurrences of the action, so it relates to the cognate-object function, not to the number of people struck.
The verb ḍarabta supplies the contextual clue.